The ordering kinetics in free and supported L10 nanoparticles was studied by means of lattice-based kinetic Monte-Carlo simulations. Starting from a fully disordered particle of Wulff shape, the simulations show that the nucleation of ordered domains is starting quickly on various (100) facets but is retarded in the particle volume due to the lack of vacancies compared with a thin film geometry. If a substrate is present, we do not find significant differences in the ordering behavior. This holds true, even if we impose a massively increased thermodynamic driving force for interface segregation, because the nucleation of ordered domains on free facets is significantly faster than the bulk diffusion of the segregating species to the interface. In cases where wetting of the substrate or surface facetting occurs, we find that diffusional atomic motion on the surface goes along with an enhanced long-range order.